Perturbation theory in Lagrangian hydrodynamics for a cosmological fluid with velocity dispersion

Takayuki Tatekawa, Momoko Suda, Kei ichi Maeda, Masaaki Morita, Hiroki Anzai

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20 Citations (Scopus)


We extensively develop a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangian description of hydrodynamics. We solve the hydrodynamic equations for a self-gravitating fluid with pressure, given by a polytropic equation of state, using a perturbation method up to second order. This perturbative approach is an extension of the usual Lagrangian perturbation theory for a pressureless fluid, in view of the inclusion of the pressure effect, which should be taken into account on the occurrence of velocity dispersion. We obtain the first-order solutions in generic background universes and the second-order solutions in a wider range of a polytropic index, whereas our previous work gives the first-order solutions only in the Einstein–de Sitter background and the second-order solutions for the polytropic index (Formula presented) Using the perturbation solutions, we present illustrative examples of our formulation in one- and two-dimensional systems, and discuss how the evolution of inhomogeneities changes for the variation of the polytropic index.

Original languageEnglish
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number6
Publication statusPublished - 2002
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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